1.72: Integration, normal and triangle area

A curve $y = f(x)$ is such that $f'(x) = 6x - 8\mathrm{e}^{2x}$. Given that the curve passes through the point $P(0, -3)$, find the equation of the curve.

The normal to the curve $y = f(x)$ at $P$ meets the line $y = 2 - 3x$ at the point $Q$. Find the area of the triangle $OPQ$, where $O$ is the origin.